QUIZ # 3 (20 pts) - SOLUTIONS
Problem 1. Find an equation of the plane tangent to the graph of
z = 3 ln(x2 y + 1) at the point where x = 1, y = 2.
Answer: z 3 ln 3 = 4(x + 1) + (y 2) or any other equivalent form.
Solution:
1. Find the value of z at the po
QUIZ # 2 - SOLUTIONS
Problem 1.(5 pts.) Find the distance between the lines
x = 2 y = z+1 and x3 = z, y = 1.
3
2
Simplify your answer as much as possible.
Problem 2. Given the curve r(t) =< t3 , 4t + 3, t2 2t > and the point
P = (1, 7, 1).
a) (5pts.) Find
QUIZ # 1 - SOLUTIONS
Problem 1.(15pts) Given a triangle
ABC with vertices
A = (2, 2, 5), B = (2, 7, 8), C = (0, 2, 5).
a) Find the cosine of the angle (BAC ).
b) Find a unit vector, perpendicular to the plane containing ABC.
NOTE: there are two dierent an
Practice Problems on Integrals 3
tan x
dx
cos4 x
9 4t 2
3)
dt
t2
ln x
dx
5)
x
2t3 + 2t + 1
7)
dx
t(t2 + 1)2
9)
sin5 x cos2 x dx
1)
11)
13)
15)
17)
19)
21)
23)
25)
ln(x + 1) dx
e cos 2x dx
x
2)
4)
6)
8)
10)
12)
14)
dt
4 + 4t2 + 3
t
16)
9
dv
81 v 4
18)
1
d
Answers to Practice Problems on Dierentiation
Most of the answers are given in a MINIMALLY simplied form (such as
combining the constants). If you solve the problem correctly, you should be
able to see that your answer matches the answer posted.
1) 2x + 1
MATH 0240 Midterm Examination I Sample 3
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages a
MATH 0240 Midterm Examination I Sample 2
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages a
MATH 0240 Midterm Examination I Sample 1
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages a